Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 262 feet and a standard deviation of 45 feet. Let X be the distance in feet for a fly ball.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly hit fly ball travels less than 304 feet. Round to 4 decimal places.

c. Find the 80th percentile for the distribution of distance of fly balls. Round to 2 decimal places.  feet

Answer 1

Solution :

Given that ,

mean = = 262

standard deviation = = 45

a.

X N (262 , 45)

b.

P(x < 304) = P[(x - ) / < (304 - 262) / 45]

= P(z < 0.93)

= 0.8238

Probability = 0.8238

c.

Using standard normal table ,

P(Z < z) = 80%

P(Z < 0.84) = 0.8

z = 0.84

Using z-score formula,

x = z * +

x = 0.84 * 45 + 262 = 299.8

80th percentile 299.8 feet